Differentially-private histogram via the Laplace mechanism — morie_dp_laplace

Adds independent Laplace(1/epsilon) noise to each bin count. Under the add-or-remove-one neighbouring-databases definition a single record participates in exactly one bin, so the per-bin sensitivity is 1 and the overall mechanism is (\(\epsilon\), 0)-DP.

Usage

morie_dp_laplace_histogram(counts, epsilon)

Arguments

counts: Integer vector of non-negative bin counts.
epsilon: Privacy budget (positive scalar).

Value

A numeric vector of the same length as counts. May contain fractional or negative values. Caller is responsible for any post-hoc non-negativity / rounding before display.

Examples

set.seed(1)
true <- c(120, 45, 8, 230, 17)

# Independent Laplace noise added to every bin.
morie_dp_laplace_histogram(true, epsilon = 0.5)
#> [1] 118.734079  44.409238   8.314961 233.390161  15.184168

# Smaller epsilon = more noise per bin.
morie_dp_laplace_histogram(true, epsilon = 0.1)
#> [1] 135.934630  67.013881  11.880117 232.987135  -3.909269

# Post-process for display: clip negatives, round to integers.
noisy <- morie_dp_laplace_histogram(true, epsilon = 1.0)
round(pmax(0, noisy))
#> [1] 119  44   8 230  18

# Release a private histogram straight from tabulated data.
counts <- as.integer(table(complaint_sample$year))
morie_dp_laplace_histogram(counts, epsilon = 1.0)
#> [1] 24998.995388     1.571349